An inexact spectral bundle method and error bounds for convex quadratic symmetric cone programming
We present an inexact spectral bundle method for solving convex quadratic symmetric cone programming (CQSCP). This method is a first-order method, hence requires much less computational cost in each iteration than second-order approaches such as interior-point methods. In each iteration of our method...
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| Format: | Thesis |
| Language: | English |
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2012
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| Online Access: | https://hdl.handle.net/10356/48908 |
| _version_ | 1826129331251838976 |
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| author | Lin, Hui Ling |
| author2 | Chua Chek Beng |
| author_facet | Chua Chek Beng Lin, Hui Ling |
| author_sort | Lin, Hui Ling |
| collection | NTU |
| description | We present an inexact spectral bundle method for solving convex quadratic symmetric cone programming (CQSCP). This method is a first-order method, hence requires much less computational cost in each iteration than second-order approaches such as interior-point methods. In each iteration of our method, we compute a largest eigenvalue inexactly, and solve a small convex quadratic symmetric cone program as a subproblem. We give a proof of the global convergence of this method using techniques from the analysis of the standard bundle method, and investigate Lipschitzian error bounds for the CQSCP problem under some mild assumptions. Finally, we describe an application of our proposed algorithm to convex quadratic semidefinite programming problems. Numerical experiments with matrices of order up to 2000 are performed, and the computational results establish the effectiveness of this method. |
| first_indexed | 2024-10-01T07:38:50Z |
| format | Thesis |
| id | ntu-10356/48908 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:38:50Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | ntu-10356/489082023-02-28T23:54:45Z An inexact spectral bundle method and error bounds for convex quadratic symmetric cone programming Lin, Hui Ling Chua Chek Beng School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Applied mathematics::Operational research We present an inexact spectral bundle method for solving convex quadratic symmetric cone programming (CQSCP). This method is a first-order method, hence requires much less computational cost in each iteration than second-order approaches such as interior-point methods. In each iteration of our method, we compute a largest eigenvalue inexactly, and solve a small convex quadratic symmetric cone program as a subproblem. We give a proof of the global convergence of this method using techniques from the analysis of the standard bundle method, and investigate Lipschitzian error bounds for the CQSCP problem under some mild assumptions. Finally, we describe an application of our proposed algorithm to convex quadratic semidefinite programming problems. Numerical experiments with matrices of order up to 2000 are performed, and the computational results establish the effectiveness of this method. DOCTOR OF PHILOSOPHY (SPMS) 2012-05-10T08:54:21Z 2012-05-10T08:54:21Z 2012 2012 Thesis Lin, Hui Ling. (2012). An inexact spectral bundle method and error bounds for convex quadratic symmetric cone programming. Doctoral thesis, Nanyang Technological University, Singapore. https://hdl.handle.net/10356/48908 10.32657/10356/48908 en 158 p. application/pdf |
| spellingShingle | DRNTU::Science::Mathematics::Applied mathematics::Operational research Lin, Hui Ling An inexact spectral bundle method and error bounds for convex quadratic symmetric cone programming |
| title | An inexact spectral bundle method and error bounds for convex quadratic symmetric cone programming |
| title_full | An inexact spectral bundle method and error bounds for convex quadratic symmetric cone programming |
| title_fullStr | An inexact spectral bundle method and error bounds for convex quadratic symmetric cone programming |
| title_full_unstemmed | An inexact spectral bundle method and error bounds for convex quadratic symmetric cone programming |
| title_short | An inexact spectral bundle method and error bounds for convex quadratic symmetric cone programming |
| title_sort | inexact spectral bundle method and error bounds for convex quadratic symmetric cone programming |
| topic | DRNTU::Science::Mathematics::Applied mathematics::Operational research |
| url | https://hdl.handle.net/10356/48908 |
| work_keys_str_mv | AT linhuiling aninexactspectralbundlemethodanderrorboundsforconvexquadraticsymmetricconeprogramming AT linhuiling inexactspectralbundlemethodanderrorboundsforconvexquadraticsymmetricconeprogramming |